On the general elephant conjecture for Mori conic bundles
Let $f:X\to S$ be an extremal contraction from a threefolds with terminal singularities onto a surface (so called Mori conic bundle). We study some particular cases of such contractions: quotients of usual conic bundles and index two contractions. Assuming Reid's general elephants conjecture we also obtain a rough classification. We present many examples.
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